( 2^0 ) 



while two qnanlitics must be measured with respect to the points s 

 of the curve, viz. its distance q from the second position of equili- 

 brium and the tangent v of the angle of inclination. 



These measurements are made with the same microscope stand I'^, 

 already mentioned in the preceding chapter, on the table of which 

 the photographic plate can be moved by screw motions in two 

 mutually perpendicular directions. 



For object-glass «i is again used or another more strongly refract- 

 ive lens, while for an eye-piece an arrangement is used which must 

 be explained now. 



At the outside of a Huygens eye-piece n". 2 a pointer is fastened. 

 When the eye-piece is turned round the optical axis, this pointer 

 moves over a circular dial, screwed on to the microscope tube and 

 divided into degrees. In this way we can read off how much the 

 eye-piece is turned in the microscope tube. Moreover in the focal 

 plane of tlie ocular lens of the eye-piece a fine cross wire is found, 

 which is so set that the crossing point lies at the centre of the field 

 of view. Hence, wiien the eye-piece is turned in the microscope 

 tube, while the crosswire turns, the crossing point will remain 

 immovable. The whole arrangement, of which the principal parts 

 have been taken from the analyser of a Zeiss polarisation microscope, 

 works very accurately and enables us to, make a number of measure- 

 ments in a short time. This is done in the following way : 



A photographic negative or better still a diapositive is placed 

 under the microscope, so that one of the directions of motion of the 

 cross table coincides with the direction of the abscissae of the photo- 

 gram. Next the whole microscope tube is again immovably screwed 

 fast at such a height that the real image of the figure to be measured 

 lies in the same plane with the wires of the eye-piece. In this way 

 one can by means of the screws of the cross table easily and quickly 

 cause the image of any point of the photogram to coincide with the 

 crossing point of the eye-piece. 



One begins with placing an absciss in the crossing point, and then 

 turns the eye-piece so that one of the two crossed wires, e. g. wire 

 A coincides with this absciss. Then an arbitrary point P of the 

 curve is placed at the crossing point. The eye-piece is now turned 

 again in such a way that the wire A forms a tangent line to the 

 curve at P. The angle through which the eye-piece must be turned 

 in order to get from the first into the second position, is the angle 

 of inclination of the curve at P. It is read on the graduated circle 

 in whole degrees, tenths being estimated. So a tangent can be drawn 

 at any point of the curve after it has been brought to the crossing 



